# Cramer is on Brilliant?

**Algebra**Level 3

\[x = \frac{\left| \begin{array}{ccc} 1 & -4 & 1\\ 5 & 1 & 2 \\ 11 & -1 & -3 \end{array} \right|}{\left| \begin{array}{ccc} 3 & -4 & 1\\ 5 & 1 & 2 \\ 1 & -1 & -3 \end{array} \right|} \quad \quad y = \frac{\left| \begin{array}{ccc} 3 & 1 & 1\\ 5 & 5 & 2 \\ 1 & 11 & -3 \end{array} \right|}{\left| \begin{array}{ccc} 3 & -4 & 1\\ 5 & 1 & 2 \\ 1 & -1 & -3 \end{array} \right|} \quad \quad z = \frac{\left| \begin{array}{ccc} 3 & -4 & 1\\ 5 & 1 & 5 \\ 1 & -1 & 11 \end{array} \right|}{\left| \begin{array}{ccc} 3 & -4 & 1\\ 5 & 1 & 2 \\ 1 & -1 & -3 \end{array} \right|} \]

Using Cramer's rule, which equation is not solved by the solutions above?

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